I would have you understand that I am all for recycling. Use it up, wear it out, make it do or do without--it was sound advice during World War II, and it still is today. Still, despite my committment to sustainable blogging, I was not pleased to see the Center on Budget and Policy Priorities reissue the graph I blogged about last year in virtually the same form.

I didn't think much of this graph at the time, and I still don't. The effect of the graph is to make it seem as if we could, by simply refusing to extend the Bush tax cuts on high earners, cover virtually all of the Social Security shortfall that is going to be putting immense pressure on the budget deficit over the next century. But this is not the case.

The CBPP gets its figure by taking present values of the Bush upper income tax cuts extended over 75 years, and comparing them to the present value of the Social Security shortfall. For those who haven't taken finance classes, present values are sort of like compound interest, in reverse. Instead of adding up the future gains from interest rates, you discount future cash flows by a discount rate. Why do this? Mostly because of a financial truism: a dollar today is worth more than a dollar tomorrow: it's certain, not risky, and while you can only use a dollar tomorrow, erm, tomorrow, you can use today's dollar either immediately, or at any time in the future.

Present value is a very useful tool for comparing different investment projects. Say you have one investment project that gives you an immediate return, and one that will give you a much higher return eventually, but takes ten years to pay off--a present value calculation lets you assess which project is actually going to be worth more.

But present value has some drawbacks, too. Our contractor was over last night trying to shore up some joists in our basement that were inappropriately cut to run electric wire, and I mentioned to him that I was working on this post. He thought for a minute, and then summed it up perfectly: "It seems to me that you've got two main problems here: liquidity constraint, and an inappropriate discount rate." Just so. Let me see if I can unpack that a little.

Because it discounts future dollars, often quite heavily, cash flows which happen beyond 10-20 years out virtually disappear. In this case, I assume that the CBPP used the same 5.25% discount rate that it used last year. Just to illustrate what the effect of that discount rate is, if you had a guaranteed $100 payment every year for the next 75 years, discounted at 5.25%, the present value of that cash flow would be $1864, versus the $7500 you get from just adding them all together. Over half of that present value comes from the first 14 years of the 75-year period. By twenty years out, that $100 is only worth $35 a year to you.

Now let's assume that someone comes along and offers me a deal: I can buy that guaranteed $100 cash flow, worth $1864, by taking out a loan. That loan has no interest payments for the first 30 years, and then I have to pay back $400 a year from year 30 to year 75. Should I do it?

Present value would say yes! The present value of those future $400 payments is only $1563, much less than the present value of my $100 annual payments that start now. But obviously, I am going to have trouble in year 30 covering my $400 payment with the $100 I am taking in every year.

The difference could be made up in savings; if I could save all my $100 payments at a guaranteed interest rate of 5.25%, then by year 30, the interest on my savings would be $382; using a combination of interest and slow withdrawals, I could pay off the loan and still have $4500 in the bank.

But the government does not borrow and save like normal people--its constraints are different. The closest it can come to saving is to pay off debt. And our debt is not yielding 5.25% right now; our highest-yielding debt is paying 4.375%, which the government is trying to sell more of, not pay off, in order to lengthen the average time-to-maturity of the debt held by the public, which lowers the risks to the Treasury of a sudden interest rate spike.

The average interest rate on debt held by the public is around 3% right now; it hasn't been as high as 3.75% since April 2009.

Now, you might say that this is not an ordinary time, and that when we pay off our debt in the future, we will get a better "return" on our savings. But remember that discount rate: it means that the immediate future is what gives you the most bang for your buck. And we've only got nine years of "savings" before the Social Security shortfall becomes larger than the cost of the Bush tax cuts, as this graph from the invaluable Committee for a Responsible Federal Budget points out:

We're not going to let the Bush tax cuts expire until 2012 at this point, which gives us 2013-9 to save by paying off debt. Let's say that you think that interest rates are going to bounce back to the 4.96 we paid in July of 2007, and we will use all of the money gained from repeal to pay down debt. By my extremely generous estimates (adding in my best estimate of other tax provisions that primarily benefit the rich, and which CBPP claims were not included in the Congressional Budget Office's $700 billion 10-year price tag for the repeal of the high-income tax cuts), by the end of the seven year period we might pay off as much as $600 billion dollars worth of debt. That's not nothing! Which is why we should never have extended the Bush tax cuts for anyone.

But at 5% average interest rates, we'd be saving less than $30 billion a year in interest. Add that to the $80 billion or so the high-income tax cuts will cost us in 2020 and you get $110 billion a year, or about 0.48% of GDP by my calculations. But in 2020, as you can see from the graph, the Social Security shortfall is 0.51% of GDP. By 2025 it hits around 1% of GDP.

Maybe you think interest rates will jump even further? It's certainly possible. But if you think this, then I assume you aren't among the people making fun of the invisible bond vigilantes, or demanding that we borrow more money for stimulus. Assuming that inflation is not going to suddenly zoom to 5% without Ben Bernanke noticing (or reacting), if you think that interest rates are going to hit 7% in 2013, that means you think that the bond market is going to freak out and raise our real interest rates by hundreds of basis points. Given that the average maturity of our debt is currently less than five years, that means we're going to have to roll over a bunch of debt paying less than 3% for a bunch of debt paying more than 7% . . . which to my ears is the same as shrieking "We're screwed!"

Last year I caught a lot of flak for pointing out that most of the heavy lifting was being done by the discounting, and that if you just looked at the cash flows, there wasn't any good way to pay for Social Security over the next 75 years just by repealing the Bush tax cuts for the rich. But you can see this point illustrated in the CBPP's own graph. At right, you'll see their graph from last year. Notice anything different about it from the one above? I mean, other than the fact that they included the cost of all the Bush tax cuts, not just the ones for high earners?

That's right, last year the costs were equal. This year, the Social Security shortfall is almost 15% larger--0.8% of GDP rather than 0.7%. That's the effect of just one year of poor economic growth, and one year closer to the point where the lines cross on that CFRB graph. That alone tells you how much the timing differences in the cash flows are affecting their results, and why this is not a very useful chart.

There's another problem, one which the CFRB points out in its excellent post on the dangers of this comparison. Actually, they too have recycled--they pointed out exactly the same thing last year when the CBPP debuted the graph. Which is that the CBPP's numbers are incredibly sensitive to initial assumptions about the growth rates in these two budget items.

That's not such a problem with Social Security, where the projections are among the most stable we can make. Demographic change is a slow moving disaster. To a first approximation, every single person who will be collecting benefits in 2030 is now living and working in the United States. And the benefits are tied to the taxes that are paid, which means that unless you think we're going to get a giant burst of immigration, the deficit isn't going to widen or narrow overmuch. Furthermore, the benefits are indexed to wages, which means, broadly, to productivity and GDP growth, so there aren't going to be huge upside or downside surprises.

The estimates of the cost of the Bush tax cuts, however, are extraordinarily sensitive to initial assumptions:, as they pointed out last year:

Essentially, CBPP assumes that the growth rates in revenue loss from 2017 through 2020 will continue forever. Over time, the compounding effects of these growth rates are significant -- increasing the value of the cuts to about 1.1 percent of GDP by 2080. Yet tiny changes in some of the numbers they use can drastically alter this number.

For example, they estimate that the tax cuts will cost $99 billion in 2017 and $120 billion in 2020 based off of a combination of Treasury and TPC estimates. We used some TPC tables to estimates these numbers at $102 billion in 2017 and the same $120 billion in 2020. When we tried to roughly apply their methodology using our $102 billion instead of their $99 billion (in other words, a nominal growth rate of about 5.6% instead of 6%) we found that the shortfall only reaches about 0.65 percent of GDP rather than 1.1 percent.

This is not to say that our $102 billion is right and their $99 billion is wrong - both are plausible and surely both will be wrong. The point is that tiny changes in these numbers cause wild swings in the ultimate cash flow results. (Though the magnitude of the present value cost wouldn't swing nearly as much - under the scenario we presented, the present value of the upper-income cuts would be between 0.5 and 0.6 percent of GDP rather than 0.7 percent).

We also tried projecting forward two other ways: assuming that the upper income tax cuts remained a fixed proportion of total revenue under CBO's extended baseline scenario and assuming bracket creep for the upper-income cuts in line with the total bracket creep we estimate in our CRFB baseline.

Here are the results:

The CBPP is entirely right to point out that the Bush tax cuts were extremely costly. Given our parlous fiscal condition, we cannot afford to extend them--we couldn't in 2010, either, but we did it anyway, and that's water under the bridge. Come 2012, they need to expire. But this is what the CBO says our budget looks like if the Bush tax cuts for high earners expire, but the rest of the budget is business-as-usual: "fixing" the AMT and Medicare doctor reimbursement rates, easing the cutbacks made by ObamaCare, and otherwise acting the way we've acted for the last decade:

This is obviously not sustainable. And much of it is simply driven by the growing ratio of retirees to workers, requiring ever-more Social Security and Medicare dollars to sustain them.

That's why I think it's a terrible idea to juxtapose the Bush tax cuts for the wealthy and Social Security in a graph that implies that the costs are roughly the same size. Not just because they're not really equivalent--but because we don't have that money to spend. We're already assuming that we let those tax cuts go in 2012, and the budget picture is still a disaster.

Easing the budget pressure from Social Security is going to require finding new revenue, or new cuts to existing programs--we can't solve the shortfall with revenues we've already spent, any more than you can pay the mortgage with the check you sent to the electric company last week. And those revenues and cuts will have to be large. It is not helpful to imply otherwise. The American public is already unwilling to confront the actual costs of the programs it has. They don't need any more encouragement to push their heads ever deeper into the sand.

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